Darboux transformation of the general Hirota equation: multisoliton solutions, breather solutions, and rogue wave solutions
نویسندگان
چکیده
منابع مشابه
Rogue waves and rational solutions of the Hirota equation.
The Hirota equation is a modified nonlinear Schrödinger equation (NLSE) that takes into account higher-order dispersion and time-delay corrections to the cubic nonlinearity. In describing wave propagation in the ocean and optical fibers, it can be viewed as an approximation which is more accurate than the NLSE. We have modified the Darboux transformation technique to show how to construct the h...
متن کاملRogue - wave pair and dark - bright - rogue wave solutions of the coupled Hirota equations ∗
Novel explicit rogue wave solutions of the coupled Hirota equations are obtained by using the Darboux transformation. In contrast to the fundamental Peregrine solitons and dark rogue waves, we present an interesting rogue-wave pair that involves four zero-amplitude holes for the coupled Hirota equations. It is significant that the corresponding expressions of the rogue-wave pair solutions conta...
متن کاملSecond-order nonlinear Schrödinger equation breather solutions in the degenerate and rogue wave limits.
We present an explicit analytic form for the two-breather solution of the nonlinear Schrödinger equation with imaginary eigenvalues. It describes various nonlinear combinations of Akhmediev breathers and Kuznetsov-Ma solitons. The degenerate case, when the two eigenvalues coincide, is quite involved. The standard inverse scattering technique does not generally provide an answer to this scenario...
متن کاملBreather and rogue wave solutions of a generalized nonlinear Schrödinger equation.
In this paper, using the Darboux transformation, we demonstrate the generation of first-order breather and higher-order rogue waves from a generalized nonlinear Schrödinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describe the soliton-type nonlinear excitations i...
متن کاملExact Multisoliton Solutions of General Nonlinear Schrödinger Equation with Derivative
Multisoliton solutions are derived for a general nonlinear Schrödinger equation with derivative by using Hirota's approach. The dynamics of one-soliton solution and two-soliton interactions are also illustrated. The considered equation can reduce to nonlinear Schrödinger equation with derivative as well as the solutions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2016
ISSN: 1687-1847
DOI: 10.1186/s13662-016-0780-z